Self-Driving Car Engineer Nanodegree¶
Deep Learning¶
Project: Build a Traffic Sign Recognition Classifier¶
In this notebook, a template is provided for you to implement your functionality in stages which is required to successfully complete this project. If additional code is required that cannot be included in the notebook, be sure that the Python code is successfully imported and included in your submission, if necessary. Sections that begin with 'Implementation' in the header indicate where you should begin your implementation for your project. Note that some sections of implementation are optional, and will be marked with 'Optional' in the header.
In addition to implementing code, there will be questions that you must answer which relate to the project and your implementation. Each section where you will answer a question is preceded by a 'Question' header. Carefully read each question and provide thorough answers in the following text boxes that begin with 'Answer:'. Your project submission will be evaluated based on your answers to each of the questions and the implementation you provide.
Note: Code and Markdown cells can be executed using the Shift + Enter keyboard shortcut. In addition, Markdown cells can be edited by typically double-clicking the cell to enter edit mode.
Step -1: Import dependencies¶
In [1]:
# Import dependencies
import numpy as np
import tensorflow as tf
from tensorflow.contrib.layers import flatten
import pickle
import math
import random
import csv
import matplotlib.pyplot as plt
import matplotlib.gridspec as gridspec
import pandas as pd
from sklearn.utils import shuffle
from skimage import transform as transf
from sklearn.model_selection import train_test_split
from IPython.display import display
import time as time
from datetime import datetime
import cv2
# Visualizations will be shown in the notebook.
%matplotlib inline
RAND_SEED = 20
Step 0: Load The Data¶
In [2]:
# Load pickled data
training_file = 'data/traffic-signs-data/train.p'
testing_file = 'data/traffic-signs-data/test.p'
with open(training_file, mode='rb') as f:
train = pickle.load(f)
with open(testing_file, mode='rb') as f:
test = pickle.load(f)
features_train, labels_train = train['features'], train['labels']
features_test, labels_test = test['features'], test['labels']
Step 1: Dataset Summary & Exploration¶
The pickled data is a dictionary with 4 key/value pairs:
'features'is a 4D array containing raw pixel data of the traffic sign images, (num examples, width, height, channels).'labels'is a 2D array containing the label/class id of the traffic sign. The filesignnames.csvcontains id -> name mappings for each id.'sizes'is a list containing tuples, (width, height) representing the the original width and height the image.'coords'is a list containing tuples, (x1, y1, x2, y2) representing coordinates of a bounding box around the sign in the image. THESE COORDINATES ASSUME THE ORIGINAL IMAGE. THE PICKLED DATA CONTAINS RESIZED VERSIONS (32 by 32) OF THESE IMAGES
Complete the basic data summary below.
In [3]:
### Replace each question mark with the appropriate value.
# TODO: Number of training examples
n_train = len(features_train)
# TODO: What's the shape of an traffic sign image?
_, IMG_HEIGHT, IMG_WIDTH, IMG_DEPTH = features_train.shape
image_shape = (IMG_HEIGHT, IMG_WIDTH, IMG_DEPTH)
# TODO: How many unique classes/labels there are in the dataset.
with open('signnames.csv', 'r') as sign_name:
reader = csv.reader(sign_name)
sign_names = list(reader)
sign_names = sign_names[1::] # Remove csv header
NUM_CLASSES = len(sign_names)
print('Total number of classes: {}'.format(NUM_CLASSES))
n_classes = len(np.unique(labels_train))
assert (NUM_CLASSES == n_classes), '1 or more class(es) not represented in training set'
# TODO: Number of testing examples.
n_test = len(labels_test)
print("Number of training examples =", n_train)
print("Number of testing examples =", n_test)
print("Image data shape =", image_shape)
print("Number of classes =", n_classes)
Visualize the German Traffic Signs Dataset using the pickled file(s). This is open ended, suggestions include: plotting traffic sign images, plotting the count of each sign, etc.
The Matplotlib examples and gallery pages are a great resource for doing visualizations in Python.
NOTE: It's recommended you start with something simple first. If you wish to do more, come back to it after you've completed the rest of the sections.
In [4]:
# Data exploration: Visualization
def visualise_random_images(num_rows, num_cols, X_dataset, y_dataset):
plt.figure(figsize = (10, 8))
# Use GridSpec to easily create a grid of images with spacing
gs = gridspec.GridSpec(num_rows, num_cols)
gs.update(wspace=0.2, hspace=0.01)
for i in range(num_rows * num_cols):
splot = plt.subplot(gs[i])
plt.axis('on')
# No ticks in the subplots
splot.set_xticklabels([])
splot.set_yticklabels([])
# Choose label at random from y_dataset
idx_rand = np.random.randint(1, len(y_dataset))
plt.imshow(X_dataset[idx_rand])
plt.annotate(str(y_dataset[idx_rand]), xy=(2, 5), color='red', fontsize='14')
plt.axis("off")
plt.show()
In [5]:
# def visualise_random_images_gray(num_rows, num_cols, X_dataset, y_dataset):
# print(X_dataset.shape)
# plt.figure(figsize = (10, 8))
# # Use GridSpec to easily create a grid of images with spacing
# gs = gridspec.GridSpec(num_rows, num_cols)
# gs.update(wspace=0.2, hspace=0.01)
# for i in range(num_rows * num_cols):
# splot = plt.subplot(gs[i])
# plt.axis('on')
# # No ticks in the subplots
# splot.set_xticklabels([])
# splot.set_yticklabels([])
# # Choose label at random from y_dataset
# idx_rand = np.random.randint(1, len(y_dataset))
# plt.imshow(X_dataset[idx_rand], cmap='gray')
# plt.annotate(str(y_dataset[idx_rand]), xy=(2, 5), color='red', fontsize='14')
# plt.axis("off")
# plt.show()
In [6]:
# Visualise 20 examples selected randomly from the training dataset
visualise_random_images(4, 5, features_train, labels_train)
In [7]:
# DATA EXPLORATION: Pixel intensity distribution
def pick_random_images_from_class(classid, num_images=5, channel=-1):
# Sanity checks
assert channel < 3, 'Channel should be between 0 and 2'
assert (np.sum(labels_train==classid)) >= num_images, 'Reduce number of images.'
# Find all images with the selected class
all_images = np.ravel(np.argwhere(labels_train==classid))
# Pick 5 images randomly
rand_image_ids = np.random.choice(all_images, size=num_images, replace=False)
rand_images = features_train[rand_image_ids, :, :, :] if channel < 0 else features_train[rand_image_ids, :, :, channel]
return rand_image_ids, rand_images
def pixel_intensity_dist(classid, channel, hist_labels_max=50, num_images=5, preprocess=False):
# Sanity checks
assert channel < 3, 'Channel should be between 0 and 2'
rand_image_ids, rand_images = pick_random_images_from_class(classid, num_images, channel)
print('Showing pixel distribution of channel {} for {} image(s) from the class {}...'
.format(channel, num_images, classid))
plt.figure(figsize=(10, 8))
gs = gridspec.GridSpec(num_images, 2)
gs.update(wspace=0.001, hspace=0.2)
for i in range(num_images):
# Plot image
splot = plt.subplot(gs[i, 0]) # First col of grid
# No ticks in the subplots
splot.set_xticklabels([])
splot.set_yticklabels([])
if preprocess:
rand_images[i] = cv2.equalizeHist(rand_images[i])
plt.imshow(rand_images[i], cmap='gray') # Change to grayscale for easily visualisation
plt.axis('off')
# Plot histogram
splot = plt.subplot(gs[i, 1]) # Second col of grid
splot.hist(np.histogram(rand_images[i], bins=256), bins=256)
splot.set_xlim([0, 100])
splot.set_ylim([0, hist_labels_max])
plt.show()
#pixel_intensity_dist(classid=10, channel=1)
In [8]:
print("### Before equalising image")
# np.random.seed(5)
pixel_intensity_dist(classid=10, channel=2, hist_labels_max=25)
In [9]:
print("### After equalising image")
# np.random.seed(5)
pixel_intensity_dist(classid=10, channel=2, hist_labels_max=25, preprocess=True)
Observations¶
From the above analysis of the dataset, I noticed variations between the images.
- Brightness and contrast are not uniform.
- The background of the signs are varied in colour and content.
- The size of the traffic sign are varied compared to the size of the image.
- The histogram distribution of the images from the same class are very different.
- Distribution of the labels are not uniform. Some signs occur more frequently than others as will be discussed in other steps below.
Step 2: Design and Test a Model Architecture¶
Design and implement a deep learning model that learns to recognize traffic signs. Train and test your model on the German Traffic Sign Dataset.
There are various aspects to consider when thinking about this problem:
- Neural network architecture
- Play around preprocessing techniques (normalization, rgb to grayscale, etc)
- Number of examples per label (some have more than others).
- Generate fake data.
Here is an example of a published baseline model on this problem. It's not required to be familiar with the approach used in the paper but, it's good practice to try to read papers like these.
NOTE: The LeNet-5 implementation shown in the classroom at the end of the CNN lesson is a solid starting point. You'll have to change the number of classes and possibly the preprocessing, but aside from that it's plug and play!
Implementation¶
Use the code cell (or multiple code cells, if necessary) to implement the first step of your project. Once you have completed your implementation and are satisfied with the results, be sure to thoroughly answer the questions that follow.
In [10]:
### Preprocess the data here.
### Feel free to use as many code cells as needed.
def preprocess_image(image, display_images = False):
# image_eq = image
# Histogram equalisation to remove effect
# image_eq = np.empty(image.shape, dtype=image.dtype)
image_eq = cv2.equalizeHist(image)
#Normalise the values
image_norm = image_eq/255.0 - 0.5
if display_images:
# Plot the results
fig = plt.figure()
grid = plt.subplot(1, 3, 1)
grid.set_title('Original Image')
grid.imshow(image, cmap='gray')
grid = plt.subplot(1, 3, 2)
grid.set_title('Equalised Histogram')
grid.imshow(image_eq, cmap='gray')
grid = plt.subplot(1, 3, 3)
grid.set_title('Normalized')
grid.imshow(image_norm, cmap='gray')
plt.tight_layout()
plt.show()
return image_norm
def preprocess_dataset(dataset):
n_imgs, img_height, img_width, _ = dataset.shape
processed_dataset = np.zeros((n_imgs, img_height, img_width, 1))
#print("dataset.shape: {}, processed_dataset.shape: {}".format(dataset.shape, processed_dataset.shape))
for i in range(len(dataset)):
img = dataset[i]
gray = cv2.cvtColor(img, cv2.COLOR_RGB2GRAY)
processed_dataset[i, :, :, 0] = preprocess_image(gray)
return processed_dataset
In [11]:
# np.random.seed(5)
rand_img_ids, rand_images = pick_random_images_from_class(10, 1)
for img in rand_images:
gray = cv2.cvtColor(img, cv2.COLOR_RGB2GRAY)
print(gray.shape)
__ = preprocess_image(gray, True)
Question 1¶
Describe how you preprocessed the data. Why did you choose that technique?
Answer: Preprocessing of the data were done in the following steps:
- Original RGB images were converted to Grayscale.
- Histogram equalisation was applied on the grayscale image so that the effect of brightness is removed and improves the contrast in the image by broadening the distribution of the histogram.
- Scaling the images between -0.5 and 0.5, dividing by 255 i.e. the maximum pixel intensity available in RGB colour space, and subtracting 0.5. This helps normalise the pixel intensities of the dataset but preserving any variation in the histogram from image to image.
In [12]:
### Generate data additional data (OPTIONAL!)
### and split the data into training/validation/testing sets here.
### Feel free to use as many code cells as needed.
def transform_image(image, angle, shear, translation):
# Rotation
ang_rot = np.random.uniform(angle) - angle/2
rows, cols, color_channels = image.shape
rotation_matrix = cv2.getRotationMatrix2D((cols/2, rows/2), ang_rot, 1)
# Translation
trans_x = translation*np.random.uniform() - translation/2
trans_y = translation*np.random.uniform() - translation/2
translation_matrix = np.array([[1, 0, trans_x], [0, 1, trans_y]]).astype('float32')
# Shearing
pts1 = np.array([[5, 5], [20, 5], [5, 20]]).astype('float32')
pt1 = 5 + shear*np.random.uniform() - shear/2
pt2 = 20 + shear*np.random.uniform() - shear/2
pts2 = np.float32([[pt1, 5], [pt2, pt1], [5, pt2]])
shear_matrix = cv2.getAffineTransform(pts1, pts2)
# Affine Transformation: Rotation + Translation + Shearing
image = cv2.warpAffine(image, rotation_matrix, (cols, rows))
image = cv2.warpAffine(image, translation_matrix, (cols, rows))
image = cv2.warpAffine(image, shear_matrix, (cols, rows))
return image
In [13]:
orig_image = features_train[n_classes, ...]
# Rotate image
transformed = transform_image(orig_image, 20, 10, 5)
splot = plt.subplot(1, 2, 1)
splot.set_title('Original Image')
plt.imshow(orig_image, cmap='gray')
splot = plt.subplot(1, 2, 2)
splot.set_title('After transformation')
plt.imshow(transformed, cmap='gray')
plt.tight_layout()
In [14]:
def augment_synthetic_data(features_data, labels_data, expand_to):
n_classes = len(np.unique(labels_data))
_, img_height, img_width, img_depth = features_data.shape
# Number of images per class
imgs_per_class = np.zeros(n_classes)
for cls in range(n_classes):
imgs_per_class[cls] = np.sum(labels_data == cls)
# Expand current class to expand_to images
new_images_per_class = expand_to - imgs_per_class
total_new_images = np.sum(new_images_per_class)
# Initialize datastructure to store new images with expanded dimension
features_new = np.zeros((int(total_new_images), img_height, img_width, img_depth), dtype=features_data.dtype)
labels_new = np.zeros(int(total_new_images))
start_id = 0
print('features_data: {}, Augmenting synthetic data...'.format(features_data.shape))
for cur_class in range(n_classes):
# Number of new images to generate of this current class
n_new_imgs = new_images_per_class[cur_class]
end_id = start_id + n_new_imgs
# Get ids of all images that belongs to cur_class
all_imgs_id = np.argwhere(labels_data == cur_class)
# Store all the new images of this current class
new_imgs_cur_class = np.zeros((int(n_new_imgs), img_height, img_width, img_depth))
for cur_new_img_id in range(int(n_new_imgs)):
# Pick a random original image that belongs to cur_class:
rand_id = np.random.choice(all_imgs_id[0], size=None, replace=True)
rand_img = features_data[rand_id]
# Do random image transform
new_img = transform_image(rand_img, 20, 10, 5)
new_imgs_cur_class[cur_new_img_id, :, :, :] = new_img
# Update new datastructure with images and its correct labels
features_new[int(start_id) : int(end_id)] = new_imgs_cur_class
labels_new[int(start_id) : int(end_id)] = np.ones((int(n_new_imgs),)) * cur_class
start_id = end_id
features_train_augmented = np.concatenate((features_data, features_new.astype('uint8')), axis=0)
labels_train_augmented = np.concatenate((labels_data, labels_new), axis=0)
print('Total new images added to dataset: {}, features_train_augmented: {}'.format(int(total_new_images),
features_train_augmented.shape))
del features_new, labels_new # Free up some memory
return [features_train_augmented, labels_train_augmented]
In [15]:
# Shuffle train dataset before splitting
features_train, labels_train = shuffle(features_train, labels_train)
_, IMG_HEIGHT, IMG_WIDTH, IMG_DEPTH = features_train.shape
# Split into train and validation set with ratio 80-20
# Train/Validation split must be done before data augmentation so that validation set
# has images similar to test set (no synthetic images)
features_train, features_validation, labels_train, labels_validation = train_test_split(features_train,
labels_train,
test_size=0.20,
random_state=RAND_SEED)
print('Training set size: {} | Validation set size: {}'.format(features_train.shape[0], features_validation.shape[0]))
# Run data augmentation on Train set to have uniform distribution of class
features_train_augmented, labels_train_augmented = augment_synthetic_data(features_train, labels_train, expand_to=4000)
In [16]:
# Data Exploration: class distribution
def class_distribution(labels):
label, count = np.unique(labels, return_counts=True)
label_freq = np.array((label, count)).T
# Sort by frequency
label_freq_sorted = sorted(label_freq, key=lambda col: col[1])
# Use pandas lib to read sign names into data frame and integrate frequency.
df_cdist = pd.read_csv('signnames.csv')
df_cdist['Frequency'] = pd.Series(np.asarray(label_freq).T[1], index=np.array(label_freq_sorted).T[0])
df_cdist = df_cdist.sort_values(by=['Frequency'], ascending=[False]).reset_index().drop('index', 1)
return (label, df_cdist)
In [17]:
augmented_train_clabel, augmented_train_df_cdist = class_distribution(labels_train_augmented)
display(augmented_train_df_cdist)
# # Visualise class distribution
# fig = plt.figure(figsize=(8, 4))
# plt.bar(augmented_train_clabel, height=augmented_train_df_cdist["Frequency"])
In [18]:
validation_clabel, validation_df_cdist = class_distribution(labels_validation)
display(validation_df_cdist)
# Visualise class distribution
fig = plt.figure(figsize=(8, 3))
plt.bar(validation_clabel, height=validation_df_cdist["Frequency"])
Out[18]:
Question 2¶
Describe how you set up the training, validation and testing data for your model. Optional: If you generated additional data, how did you generate the data? Why did you generate the data? What are the differences in the new dataset (with generated data) from the original dataset?
Answer:
- The original dataset was split by 80% into training and 20% into validation sets using train_test_split function from sklearn lib.
- Since the number of images per label was not uniform and because the training set size was too small to sufficiently train a convolutional network, all labels were expanded up to 4000 examples by synthetically generated data using augment_synthetic_data() function below.
- As part of augmenting synthetic data, the image jittering was performed. For this affine transformation was applied: where the images were rotated by random number generated between +/- 20 degrees, translated by +/-5 pixels along both vertical and horizontal directions, and finally sheared by +/-10 pixels. This was to ensure sufficient resiliency and affine invarience when evaluated against unknown test data. Choice of rotation angle was chosen keeping in mind that too much rotation could change the meaning of some traffic signs such as that having arrows. At the same time, it would benefit from being rotation invariant to a certain degree.
In [19]:
def plot_loss(summary_train):
fig, ax = plt.subplots(1, 3, figsize=(15, 3))
plt.subplots_adjust(wspace = .2)
for i in range(len(ax)):
ax[i].tick_params(axis='x', labelsize=12)
ax[i].tick_params(axis='y', labelsize=12)
ax[i].xaxis.label.set_fontsize(12)
ax[i].yaxis.label.set_fontsize(12)
marker_size = 8
ax[0].plot(summary_train[:,0], summary_train[:,1], 'b-o', markersize=marker_size, label='Train')
ax[0].plot(summary_train[:,0], summary_train[:,2], 'r-o', markersize=marker_size, label='Validation')
ax[0].set_xlabel('Epoch')
ax[0].set_ylabel('Accuracy')
ax[1].semilogy(summary_train[:,0], summary_train[:,3], 'b-o', markersize=marker_size, label='Train')
ax[1].semilogy(summary_train[:,0], summary_train[:,4], 'r-o', markersize=marker_size, label='Validation')
ax[1].set_xlabel('Epoch')
ax[1].set_ylabel('Loss')
ax[2].semilogy(summary_train[:,0], summary_train[:,3]/summary_train[:,4], 'k-o', markersize=marker_size, label='Train')
ax[2].set_xlabel('Epoch')
ax[2].set_ylabel('Training/Validation')
plt.show()
Question 3¶
What does your final architecture look like? (Type of model, layers, sizes, connectivity, etc.) For reference on how to build a deep neural network using TensorFlow, see Deep Neural Network in TensorFlow from the classroom.
Answer: The final architecture is a ConvNet consisting of two parts:
- Three convolutional blocks, each composed of two sub-blocks of: a convolutional layer, a ReLU activation function (to prevent gradient vanishing in deep neural networks), and a dropout layer (to force the network find generalised representations) connected in series. The end of each of the three convolutional block ended with a 2x2 max pooling operation (just before the dropout operation).
- A block of two fully connected layers, each followed by a ReLU activation function and a dropout layer.
In [20]:
# Remove previous Tensors and Operations
tf.reset_default_graph()
# Initialization functions for convolutional network
def init_weights(shape, mean, stddev, name, seed=RAND_SEED):
init = tf.truncated_normal(shape, mean=mean, stddev=stddev, seed=seed, name=name+'_tnorm')
return tf.Variable(init, name=name)
def init_bias(shape, init, name):
init = tf.constant(init, shape=shape, name=name+'_const')
return tf.Variable(init, name=name)
def conv_layer(x, W, strides, padding, name):
return tf.nn.conv2d(x, W, strides=strides, padding=padding, name=name)
def max_pool(x, padding, name):
return tf.nn.max_pool(x, ksize=[1, 2, 2, 1], strides=[1, 2, 2, 1], padding=padding, name=name)
In [21]:
# Weights and biases
IMG_DEPTH = 1
mu = 0
sigma = 0.05
bias_init = 0.05
weights = {
'conv1_w': init_weights([3, 3, IMG_DEPTH, 80], mean=mu, stddev=sigma, name='conv1_w'),
'conv2_w': init_weights([3, 3, 80, 120], mean=mu, stddev=sigma, name='conv2_w'),
'conv3_w': init_weights([4, 4, 120, 180], mean=mu, stddev=sigma, name='conv3_w'),
'conv4_w': init_weights([3, 3, 180, 200], mean=mu, stddev=sigma, name='conv4_w'),
'conv5_w': init_weights([3, 3, 200, 200], mean=mu, stddev=sigma, name='conv5_w'),
'fc1_w': init_weights([800, 80], mean=mu, stddev=sigma, name='fc1_w'),
'fc2_w': init_weights([80, 80], mean=mu, stddev=sigma, name='fc2_w'),
'fc3_w': init_weights([80, 43], mean=mu, stddev=sigma, name='fc3_w'),
}
biases = {
'conv1_b': init_bias(shape=[80], init=bias_init, name='conv1_b'),
'conv2_b': init_bias(shape=[120], init=bias_init, name='conv2_b'),
'conv3_b': init_bias(shape=[180], init=bias_init, name='conv3_b'),
'conv4_b': init_bias(shape=[200], init=bias_init, name='conv4_b'),
'conv5_b': init_bias(shape=[200], init=bias_init, name='conv5_b'),
'fc1_b': init_bias([80], init=bias_init, name='fc1_b'),
'fc2_b': init_bias([80], init=bias_init, name='fc2_b'),
'fc3_b': init_bias([43], init=bias_init, name='fc3_b'),
}
In [22]:
def conv_model(input, keep_prob, keep_prob_conv, weights, biases):
# Convolutional layer 1
conv1 = conv_layer(input, weights['conv1_w'], strides=[1, 1, 1, 1], padding='VALID', name='conv1_op')
conv1_activ = tf.nn.relu(conv1 + biases['conv1_b'], name='conv1_activ')
conv1_drop = tf.nn.dropout(conv1_activ, keep_prob=keep_prob_conv, name='conv1_drop')
# Convolutional layer 2
conv2 = conv_layer(conv1_drop, weights['conv2_w'], strides=[1, 1, 1, 1], padding='SAME', name='conv2_op')
conv2_activ = tf.nn.relu(conv2 + biases['conv2_b'], name='conv2_activ')
conv2_pool = max_pool(conv2_activ, padding='VALID', name='conv2_pool')
pool2_drop = tf.nn.dropout(conv2_pool, keep_prob=keep_prob_conv, name='conv2_drop')
# Convolutional layer 3
conv3 = conv_layer(pool2_drop, weights['conv3_w'], strides=[1, 1, 1, 1], padding='VALID', name='conv3_op')
conv3_activ = tf.nn.relu(conv3 + biases['conv3_b'], name='conv3_activ')
conv3_drop = tf.nn.dropout(conv3_activ, keep_prob=keep_prob_conv, name='conv3_drop')
# Convolutional layer 4
conv4 = conv_layer(conv3_drop, weights['conv4_w'], strides=[1, 1, 1, 1], padding='SAME', name='conv4_op')
conv4_activ = tf.nn.relu(conv4 + biases['conv4_b'], name='conv4_activ')
conv4_pool = max_pool(conv4_activ, padding='VALID', name='conv4_pool')
conv4_drop = tf.nn.dropout(conv4_pool, keep_prob, name='conv4_drop')
# Convolutional layer 5
conv5 = conv_layer(conv4_drop, weights['conv5_w'], strides=[1, 1, 1, 1], padding='VALID', name='conv5_op')
conv5_activ = tf.nn.relu(conv5 + biases['conv5_b'], name='conv5_activ')
conv5_pool = max_pool(conv5_activ, padding='VALID', name='conv5_pool')
conv5_drop = tf.nn.dropout(conv5_pool, keep_prob, name='conv5_drop')
# Fully connected layer 1
fc0 = flatten(conv5_drop)
fc1 = tf.nn.relu(tf.matmul(fc0, weights['fc1_w']) + biases['fc1_b'], name='fc1')
fc1_drop = tf.nn.dropout(fc1, keep_prob, name='fc1_drop')
# Fully connected layer 2
fc2 = tf.nn.relu(tf.matmul(fc1_drop, weights['fc2_w']) + biases['fc2_b'], name='fc2')
fc2_drop = tf.nn.dropout(fc2, keep_prob, name='fc2_drop')
logits = tf.add(tf.matmul(fc2_drop, weights['fc3_w']), biases['fc3_b'], name='logits')
return [weights, logits]
In [23]:
### Train your model here.
### Feel free to use as many code cells as needed.
features = tf.placeholder(tf.float32, (None, IMG_HEIGHT, IMG_WIDTH, IMG_DEPTH), name='features')
labels = tf.placeholder(tf.int32, (None), name='labels')
keep_prob = tf.placeholder(tf.float32, name='keep_prob')
keep_prob_conv = tf.placeholder(tf.float32, name='keep_prob_conv')
one_hot_labels = tf.one_hot(labels, n_classes, name='one_hot')
rate = tf.placeholder(tf.float32, name='rate')
weights, logits = conv_model(features, keep_prob, keep_prob_conv, weights, biases)
softmax_operation = tf.nn.softmax(logits, name='softmax')
cross_entropy = tf.nn.softmax_cross_entropy_with_logits(logits, one_hot_labels, name='softmax_cross_entropy')
beta = 0.0001
loss_reg = beta * (tf.nn.l2_loss(weights['fc1_w']) + tf.nn.l2_loss(weights['fc2_w']) + tf.nn.l2_loss(weights['fc3_w']))
loss = tf.reduce_mean(cross_entropy, name='reduce_mean') + loss_reg
optimizer = tf.train.AdamOptimizer(learning_rate = rate, name='optimizer')
training_operation = optimizer.minimize(loss, name='training_operation')
In [24]:
correct_prediction = tf.equal(tf.argmax(logits, 1), tf.argmax(one_hot_labels, 1), name='correct_prediction')
accuracy_operation = tf.reduce_mean(tf.cast(correct_prediction, tf.float32), name='accuracy_operation')
def evaluate(features_data, labels_data):
num_examples = len(features_data)
total_accuracy = 0
sess = tf.get_default_session()
total_l = 0
for offset in range(0, num_examples, BATCH_SIZE):
end = offset + BATCH_SIZE
# end = end if (end <= last_index) else last_index
batch_features, batch_labels = features_data[offset:end], labels_data[offset:end]
accuracy, l = sess.run([accuracy_operation, loss],
feed_dict={features: batch_features,
labels: batch_labels,
keep_prob_conv: 1.0,
keep_prob: 1.0})
total_accuracy += (accuracy * len(batch_features))
total_l += (l * len(batch_features))
return [total_accuracy/num_examples, total_l/num_examples]
Question 4¶
How did you train your model? (Type of optimizer, batch size, epochs, hyperparameters, etc.)
Answer:
- AdamOptimzer was used as the optimizer of choice in order to minimise the loss function because it is more efficient than stochastic gradient descent.
- Batch size of 200 images as a balance between training being too slow versus memory consumption. Also, the validation accuracy of the model decreased when it was too large.
- Weights were initialised using a truncated Gaussian distribution with mean (mu) of 0 and standard deviation (sigma) of 0.05. If sigma is too low or too high, the model would hardly show any improvement (loss would go down very slowly or not at all) in learning during training.
- Learning rate was set to 0.01 as a balance between too high whereby model doesn't learn or too low where the convergence takes forever.
- Model was trained for only 25 Epochs but was surprisingly sufficient to produce good training and validation accuracies of 0.9995 and 0.9954 respectively. Initially, the model was train up to 65 epochs however, due to a bug in restoring the saved model, I couldn't afford to use too much time on the cloud GPU.
- Dropout layers with keep rate of 0.5 was used for fully connected layers, while less agressive dropout was used with a keep rate of 0.6 for convolutional layers.
- Max pooling was used to decrease the size of the output and prevent overfitting.
- L2 regularisation was applied to the weights of fully connected layers to prevent overfitting.
- The resulting plots shown below track the accuracy and the loss of the training and validation sets in each epoch during training. Loss of training set is 10 times smaller than the validation set. Last plot is the Loss ratio of Training and Validation which is observed to remain constant at higher epochs.
In [28]:
EPOCHS = 25
BATCH_SIZE = 200
model_version = 'j'
keep_rate = 0.5
keep_rate_shallow = 0.6
learn_rate = 1e-3
saver = tf.train.Saver()
with tf.Session() as sess:
sess.run(tf.global_variables_initializer())
print("Training...")
summary_train = []
print('Pre-processing training data...')
features_train_processed = preprocess_dataset(features_train_augmented)
print('features_train pre-processed datatset size: {} | dtype: {}'.format(features_train_processed.shape,
features_train_processed.dtype))
print('Pre-processing validation data...')
features_val_processed = preprocess_dataset(features_validation)
print('features_validation pre-processed datatset size: {} | dtype: {}'.format(features_val_processed.shape,
features_val_processed.dtype))
start_time = time.time()
labels_train_processed = None
for i in range(EPOCHS):
# Randomise training dataset before training
if labels_train_processed is None:
# first time only
features_train_processed, labels_train_processed = shuffle(features_train_processed, labels_train_augmented)
else:
features_train_processed, labels_train_processed = shuffle(features_train_processed, labels_train_processed)
# Train processed data
num_examples = len(features_train_processed)
# last_index = num_examples - 1
# Train model in batches
for offset in range(0, num_examples, BATCH_SIZE):
end = offset + BATCH_SIZE
# end = end if (end <= last_index) else last_index
batch_features, batch_labels = features_train_processed[offset:end], labels_train_processed[offset:end]
sess.run(training_operation, feed_dict={features: batch_features,
labels: batch_labels,
keep_prob_conv: keep_rate_shallow,
keep_prob: keep_rate,
rate: learn_rate})
# Evaluate against training data
print('Evaluating training data...')
train_accuracy, train_loss = evaluate(features_train_processed, labels_train_processed)
# Evaluate against validation data
print('Evaluating validation data...')
validation_accuracy, validation_loss = evaluate(features_val_processed, labels_validation)
print("--- EPOCH {} ---".format(i+1))
print("Train accuracy: {:.4f} | Validation accuracy = {:.4f}".format(train_accuracy, validation_accuracy))
print("Train loss: {:.5f} | Validation loss = {:.5f}".format(train_loss, validation_loss))
summary_train.append([i+1, train_accuracy, validation_accuracy, train_loss, validation_loss])
cur_time_diff = str((time.time() - start_time) / 60.0)
# Example: '2017-01-03 17:45:35.177000'
cur_summary_train = np.array([i+1, train_accuracy, validation_accuracy,
train_loss, validation_loss,
str(datetime.now()), cur_time_diff])
np.save('cur_summary_train_' + model_version + '.npy', cur_summary_train)
if (i % 10) == 0:
model_filename = 'conv_model_' + model_version + '_' + str(i)
saver.save(sess, model_filename)
print("Model {} saved.".format(model_filename))
end_time = time.time()
time_diff = end_time - start_time
print('Time taken: {} seconds = {} minutes'.format(time_diff, time_diff / 60.0))
summary_train = np.array(summary_train)
np.save('summary_train_' + model_version + '.npy', summary_train)
saver.save(sess, 'conv_model_' + model_version + '_final')
print('Final Model saved.')
# Plot loss
plot_loss(summary_train)
In [ ]:
# Plot loss
summary_train_loaded = np.load('summary_train_j.npy')
plot_loss(summary_train_loaded)
In [ ]:
# from tensorflow.python.tools.inspect_checkpoint import print_tensors_in_checkpoint_file
# # List ALL tensors.
# print_tensors_in_checkpoint_file(file_name='./conv_model_j_final', tensor_name='')
# for v in tf.get_collection(tf.GraphKeys.GLOBAL_VARIABLES):
# print(v)
In [30]:
### Load the images and plot them here.
### Feel free to use as many code cells as needed.
# import tensorflow as tf
# tf.reset_default_graph()
model_file = 'conv_model_j_final'
BATCH_SIZE = 200
saver = tf.train.Saver()
with tf.Session() as sess:
sess.run(tf.global_variables_initializer())
saver.restore(sess, './' + model_file)
print('Pre-processing training data...')
features_train_processed = preprocess_dataset(features_train_augmented)
print('features_train pre-processed datatset size: {} | dtype: {}'.format(features_train_processed.shape,
features_train_processed.dtype))
print('Pre-processing validation data...')
features_val_processed = preprocess_dataset(features_validation)
print('features_validation pre-processed datatset size: {} | dtype: {}'.format(features_val_processed.shape,
features_val_processed.dtype))
print('Pre-processing test data...')
features_test_processed = preprocess_dataset(features_test)
print('features_test pre-processed datatset size: {} | dtype: {}'.format(features_test_processed.shape,
features_test_processed.dtype))
start_time = time.time()
# Randomise training dataset before training
# features_train_processed, labels_train_processed = shuffle(features_train_processed, labels_train_augmented)
# Evaluate against training data
# train_accuracy, train_loss = evaluate(features_train_processed, labels_train_processed)
train_accuracy, train_loss = evaluate(features_train_processed, labels_train_augmented)
# Evaluate against validation data
validation_accuracy, validation_loss = evaluate(features_val_processed, labels_validation)
# Evaluate against test data
test_accuracy, test_loss = evaluate(features_test_processed, labels_test)
print("Train accuracy: {:.4f} | Validation accuracy = {:.4f} | Test accuracy = {:.4f}".format(train_accuracy,
validation_accuracy,
test_accuracy))
print("Train loss: {:.5f} | Validation loss = {:.5f}| Test loss = {:.5f}".format(train_loss,
validation_loss,
test_loss))
# Select 20 random images only instead of the whole features_test to prevent overflowing GPU for softmax_op
rand_imgs = [random.randint(0, len(labels_test)) for i in range(20)]
features_test_select = np.zeros((20, IMG_HEIGHT, IMG_WIDTH, 1))
labels_test_select = np.zeros((20, 1))
for i in range(len(rand_imgs)):
features_test_select[i] = features_test_processed[rand_imgs[i]]
labels_test_select = labels_test[rand_imgs[i]]
test_prediction_prob = sess.run(softmax_operation, feed_dict={features: features_test_select,
keep_prob_conv: 1.0,
keep_prob: 1.0})
prediction_test = np.argmax(test_prediction_prob, 1)
end_time = time.time()
time_diff = end_time - start_time
print('Time taken: {} seconds = {} minutes'.format(time_diff, time_diff/60.0))
In [ ]:
# plt.figure()
# img1 = features_train_processed[2304, :, :, 0]
# plt.imshow(img1, cmap='gray')
In [ ]:
# # Continue training from where we stopped earlier...
# epochs_start = 25
# epochs_end = 50
# BATCH_SIZE = 200
# model_version = 'j'
# keep_rate = 0.5
# keep_rate_shallow = 0.6
# learn_rate = 1e-4
# model_file = 'conv_model_' + model_version + '_final'
# summary_file = 'summary_train_' + model_version + '.npy'
# # model_file = 'conv_model_h_final'
# # model_file = 'conv_model_e_final_422.763980170091.meta'
# with tf.Session() as sess:
# sess.run(tf.global_variables_initializer())
# saver = tf.train.Saver()
# saver.restore(sess, './' + model_file)
# num_examples = len(features_train_augmented)
# print("Training...")
# summary_train = np.load(summary_file).tolist()
# print('Pre-processing training data...')
# features_train_processed = preprocess_dataset(features_train_augmented)
# print('features_train pre-processed datatset size: {} | dtype: {}'.format(features_train_processed.shape,
# features_train_processed.dtype))
# print('Pre-processing validation data...')
# features_val_processed = preprocess_dataset(features_validation)
# print('features_validation pre-processed datatset size: {} | dtype: {}'.format(features_val_processed.shape,
# features_val_processed.dtype))
# start_time = time.time()
# for i in range(epochs_start, epochs_end):
# # Randomise training dataset before training
# features_train_processed, labels_train_processed = shuffle(features_train_processed, labels_train_augmented)
# # Train processed data
# num_examples = len(features_train_processed)
# # last_index = num_examples - 1
# # Train model in batches
# for offset in range(0, num_examples, BATCH_SIZE):
# end = offset + BATCH_SIZE
# # end = end if (end <= last_index) else last_index
# batch_features, batch_labels = features_train_processed[offset:end], labels_train_processed[offset:end]
# sess.run(training_operation, feed_dict={features: batch_features,
# labels: batch_labels,
# keep_prob_conv: keep_rate_shallow,
# keep_prob: keep_rate,
# rate: learn_rate})
# # Evaluate against training data
# print('Evaluating training data...')
# train_accuracy, train_loss = evaluate(features_train_processed, labels_train_processed)
# # Evaluate against validation data
# print('Evaluating validation data...')
# validation_accuracy, validation_loss = evaluate(features_val_processed, labels_validation)
# print("--- EPOCH {} ---".format(i+1))
# print("Train accuracy: {:.4f} | Validation accuracy = {:.4f}".format(train_accuracy, validation_accuracy))
# print("Train loss: {:.5f} | Validation loss = {:.5f}".format(train_loss, validation_loss))
# summary_train.append([i+1, train_accuracy, validation_accuracy, train_loss, validation_loss])
# cur_time_diff = str((time.time() - start_time) / 60.0)
# # Example: '2017-01-03 17:45:35.177000'
# cur_summary_train = np.array([i+1, train_accuracy, validation_accuracy,
# train_loss, validation_loss,
# str(datetime.now()), cur_time_diff])
# np.save('cur_summary_train_' + model_version + '.npy', cur_summary_train)
# if (i % 10) == 0:
# try:
# saver
# except NameError:
# saver = tf.train.Saver()
# model_filename = 'conv_model_' + model_version + '_' + str(i)
# saver.save(sess, model_filename)
# print("Model {} saved.".format(model_filename))
# end_time = time.time()
# time_diff = end_time - start_time
# print('Time taken: {} seconds = {} minutes'.format(time_diff, time_diff / 60.0))
# summary_train = np.array(summary_train)
# np.save('summary_train_' + model_version + '.npy', summary_train)
# try:
# saver
# except NameError:
# saver = tf.train.Saver()
# saver.save(sess, 'conv_model_' + model_version + '_final')
# print('Final Model saved.')
# # Plot loss
# plot_loss(summary_train)
Answer:
Question 5¶
What approach did you take in coming up with a solution to this problem? It may have been a process of trial and error, in which case, outline the steps you took to get to the final solution and why you chose those steps. Perhaps your solution involved an already well known implementation or architecture. In this case, discuss why you think this is suitable for the current problem.
Answer: I researched various image identification algorithms by researchers and experimented with different types of models such as linear, fully connected network, convolutional layer. I also read a lot of discussions from the forums and that probably biased me towards using convolutional networks. The convolutional networks gave the best mix of accuracy and speed of training.
For the convolutional network, I started with one convolutional layer, and a fully connected layer and reached validation of about 0.8. I increased the depth and width of the network and found the performance of the model improving significantly through a bit of trail and error.
I also experimented with leaky ReLU activation function because of some references indicating that standard ReLU units being fragile and irreversibly die during training. However, I could not find any noticeable difference during training of my model and perhaps due to frequent bugs, I went back to standard ReLU to keep it simple.
I included dropout and L2-regularisation primarily because of prior research into its advantages of preventing overfitting.
I spent a lot of time with input in RGB colour space assuming that the network would be able to find an efficient represention of colour space by itself. However, due to model accuracy, I pre-processed the images to grayscale and found that model accuracy increased by a few points and at the same time make training faster. I found that pre-processing and augmenting randomly varying affine transformations to be the equally time consumming and crucial stage to get the accuracy higher.
The result of my final convolutional model trained only for 25 epochs is as follows:
- Train accuracy: 0.9995
- Validation accuracy = 0.9954
- Test accuracy = 0.9717
On testing the model on 20 random test images below, we can see that it incorrectly labeled Roundbout manadory (40) as Speed limit 100km/h (7). This is probably because of the image contains half a sign at the top of the roundabout sign and probably was confused. However, the model works quite effectively even for dark or blurred images. Therefore, my implementation is suitable for the current problem.
Step 3: Test a Model on New Images¶
Take several pictures of traffic signs that you find on the web or around you (at least five), and run them through your classifier on your computer to produce example results. The classifier might not recognize some local signs but it could prove interesting nonetheless.
You may find signnames.csv useful as it contains mappings from the class id (integer) to the actual sign name.
Implementation¶
Use the code cell (or multiple code cells, if necessary) to implement the first step of your project. Once you have completed your implementation and are satisfied with the results, be sure to thoroughly answer the questions that follow.
In [40]:
_, ax = plt.subplots(len(rand_imgs)//5, 5, figsize=(8, 6))
row, col = 0, 0
for i, idx in enumerate(rand_imgs):
img = features_test[idx]
ax[row, col].imshow(img, cmap='gray')
annot = 'Pred:'+str( int(prediction_test[i])) +' | True:'+ str(labels_test[idx])
ax[row, col].annotate(annot, xy=(3, 5), color='black', fontsize='7', bbox=dict(boxstyle="round", fc="0.8"))
ax[row,col].axis('off')
col += 1
if col == 5:
row += 1
col = 0
plt.show()
Question 6¶
Choose five candidate images of traffic signs and provide them in the report. Are there any particular qualities of the image(s) that might make classification difficult? It could be helpful to plot the images in the notebook.
Answer: The 30 images of 10 different labels of varying frequencies, were real images taken from Karlsruhe, Germany. One of the images were taken in very high side angle. The 30 speed limit was different because it has the word 'Zone' in it which was not available in any of the training sets. One of the 'No Entry' signs is slightly occluded by some leaves in front of it.
In [ ]:
# ## Saving new images to pickle file.
# ## The images are manually labelled.
# ## The order of the images is not guaranteed to be the same
# %matplotlib inline
# image_file_paths = listdir('test_images')
# images = []
# for path in image_file_paths:
# images.append(mpimg.imread('%s%s' % ('test_images/', path)))
# new_signs_img = np.zeros([len(images),32,32,3],dtype=np.uint8)
# new_signs_label = np.array([28,2,22,22,36,
# 13,17,1,1,17,
# 25,38,25,31,35,
# 22,25,36,38,38,
# 17,22,35,12,33,
# 38,38,25,38
# ],dtype=np.uint8)
# with open('signnames.csv', 'r') as csvfile:
# signnames = csv.reader(csvfile, delimiter=',')
# next(signnames,None)
# for row in signnames:
# signs.append(row[1])
# csvfile.close()
# plt.figure(figsize=(20,20))
# for id,img in enumerate(images):
# images[id] = cv2.resize(img,dsize=(32,32))
# new_signs_img[id] = images[id]
# sub = plt.subplot(6,5,id+1)
# plt.imshow(new_signs_img[id])
# sub.set_title("%s, %s" % (signs[new_signs_label[id]], new_signs_label[id]))
# pickle_file = 'new_signs.p'
# if not os.path.isfile(pickle_file):
# print('Saving data to pickle file...')
# try:
# with open('new_signs.p', 'wb') as pfile:
# pickle.dump(
# {
# 'data': new_signs_img,
# 'labels': new_signs_label,
# },
# pfile, pickle.HIGHEST_PROTOCOL)
# except Exception as e:
# print('Unable to save data to', pickle_file, ':', e)
# raise
# print('Data cached in pickle file.')
In [97]:
# Data exploration: Visualization
def visualise_images(num_rows, num_cols, X_dataset, y_dataset):
plt.figure(figsize = (10, 8))
# Use GridSpec to easily create a grid of images with spacing
gs = gridspec.GridSpec(num_rows, num_cols)
gs.update(wspace=0.1, hspace=0.2)
for i in range(len(X_dataset)):
splot = plt.subplot(gs[i])
plt.axis('on')
# No ticks in the subplots
splot.set_xticklabels([])
splot.set_yticklabels([])
# Choose label at random from y_dataset
if X_dataset.shape[3] == 1:
plt.imshow(X_dataset[i, :, :, 0], cmap='gray')
else:
plt.imshow(X_dataset[i])
plt.annotate(str(y_dataset[i]), xy=(2, 5), color='red', fontsize='14')
plt.axis("off")
plt.show()
In [98]:
## Load new images from pickle file
%matplotlib inline
new_signs_file = "new_signs.p"
with open(new_signs_file, mode='rb') as f:
new_signs = pickle.load(f)
f.close()
features_new = new_signs['data']
labels_new = new_signs['labels']
visualise_images(6, 5, features_new, labels_new)
In [99]:
# Pre-processing
features_new_processed = preprocess_dataset(features_new)
visualise_images(6, 5, features_new_processed, labels_new)
In [118]:
### Inference
k_top = 5
model_file = 'conv_model_j_final'
feed_dict = {features: features_new_processed, keep_prob: 1.0, keep_prob_conv: 1.0}
saver = tf.train.Saver()
with tf.Session() as sess:
saver.restore(sess, './' + model_file)
prediction_prob = sess.run(softmax_operation, feed_dict=feed_dict)
prediction = np.argmax(prediction_prob, 1)
# Top 5 probabilities
top_k_values = tf.nn.top_k(softmax_operation, k_top)
top_k_proba = sess.run([softmax_operation, top_k_values], feed_dict=feed_dict)
### Feel free to use as many code cells as needed.
# Visualize image with predicted label
print('Prediction on new data')
for i in range(len(features_new)):
plt.figure(figsize=(2, 2))
img = features_new[i]
plt.imshow(img)
plt.title("{} ({})".format(sign_names[prediction[i]][1], prediction[i]), fontsize=10)
plt.axis('off')
plt.show()
Question 7¶
Is your model able to perform equally well on captured pictures when compared to testing on the dataset? The simplest way to do this check the accuracy of the predictions. For example, if the model predicted 1 out of 5 signs correctly, it's 20% accurate.
NOTE: You could check the accuracy manually by using signnames.csv (same directory). This file has a mapping from the class id (0-42) to the corresponding sign name. So, you could take the class id the model outputs, lookup the name in signnames.csv and see if it matches the sign from the image.
Answer:
As shown in the output images above, the images were manully labelled and saved to a picket file. Since there were 5 incorrect classifications out of 30 new test images, the accuracy of the model is 83.33%.
In [117]:
### TOP 5 PROBABILITIES: CERTAINTIES
#initialize subplots
_, ax = plt.subplots(len(features_new), 2, figsize=(6, 32))
col_plot = 0
for i in range(len(features_new)):
img = features_new[i]
ax[i, col_plot].imshow(img)
ax[i,col_plot].axis('off')
col_plot += 1
ax[i, col_plot].barh(-np.arange(k_top), top_k_proba[1][0][i], align='center')
# Annotations
for k in range(k_top):
text_pos = [top_k_proba[1][0][i][k]+.1, -(k+0.4)]
ax[i, col_plot].text(text_pos[0], text_pos[1],
"{} ({})".format(sign_names[top_k_proba[1][1][i][k]][1],
sign_names[top_k_proba[1][1][i][k]][0]),
fontsize=8)
ax[i,col_plot].axis('off')
col_plot = 0
plt.show()
Question 8¶
Use the model's softmax probabilities to visualize the certainty of its predictions, tf.nn.top_k could prove helpful here. Which predictions is the model certain of? Uncertain? If the model was incorrect in its initial prediction, does the correct prediction appear in the top k? (k should be 5 at most)
Answer:
For the incorrect classifications, the model is not very certain for that label as there are other labels competing for the decision.
The incorrect labels were as follows:
- Incorrectly classified "No entry" (17) as "No passing" (9). This is probably due to the presence of background leaves as well as occluding leaves blocking the sign.
- Incorrectly classified "Speed limit (30km/h)" (1) as "Speed limit (80km/h)" (5). This is probably due to the presence of text 'Zone' which is not part of any training dataset.
- Incorrectly classified "Keep Right" (38) as "Speed limit (80km/h)" (5). This was quite challenging as the image was taken from the side at a high angle.
- Again incorrectly classified "No entry" (17) as "No passing" (9). This is probably due to the presence of background leaves as well as occluding leaves blocking the sign.
- Incorrectly classified "Ahead only" (35) as "Speed limit (60km/h)" (3). This could be due to the background noise.
Note: Once you have completed all of the code implementations and successfully answered each question above, you may finalize your work by exporting the iPython Notebook as an HTML document. You can do this by using the menu above and navigating to \n", "File -> Download as -> HTML (.html). Include the finished document along with this notebook as your submission.
Future improvements¶
- As traffic signs are designed for humans, and colour is an important component of classification, consider converting RGB images to YUV or LAB colour space so that the colour is more representative of human perception than RGB. Perhaps including grayscale as the fourth channel would help classify even better.
- Create a second output for the "category" of the traffic sign such as Danger/warning, Priority, Infomation, Direction, Position, etc. and weight the loss function based on the sign category.
Thanks to¶
- Vivek Yadav and Jean-Marc Beaujour for code snippets, Hanqui Ying for german images, CarND forum and Slack for general advice and code snippets.